X2y.py

def X2y(X, with_error = True):
    
    # functional form of the dependence between y and X
    y_star = X['linear'] + X['nonlinear_square'] ** 2 + np.sin(3 * X['nonlinear_sin']) + (X['interaction_1'] * X['interaction_2'] * X['interaction_3'])
    
    # add random error called epsilon (this will be used for creating y)
    if with_error:
        np.random.seed(0)
        epsilon = np.random.normal(0, .1, len(y_star))
        return y_star + epsilon
    
    # do not add error (this will be used for prediction)
    else:
        return y_star